Surging housing costs are the engine driving Tuesday's worrisome Consumer Price Index report — and it's going to be tough to bring them down.

Why it matters: The inflation numbers provoked a fresh round of worry that the Fed still hasn't gotten inflation under control, and that it'll have to raise interest rates quite a bit more.

Driving the news: Core U.S. inflation — that is, price increases stripping out volatile food and energy costs — jumped more than expected in August.

The big picture: Shelter costs were the single most important category driving core inflation up, as they are weighted heavily in CPI calculations.

What we're watching: Purchase prices for homes. The COVID-related housing boom pushed the median purchase price of an existing home up roughly 50%.

What they're saying: "Typically, once those major shelter components begin to gather momentum, there’s an element of inertia that tends to keep them hot for some time," says Jason Pride, chief investment officer of private wealth at Philadelphia-based money management firm Glenmede.